A296355 True position where binary expansion of n starts in the list of binary numbers in the binary Champernowne sequence A076478.

0, 1, 1, 5, 1, 6, 5, 20, 1, 17, 15, 6, 8, 5, 20, 63, 9, 1, 22, 17, 15, 55, 6, 25, 8, 21, 48, 5, 20, 27, 63, 174, 9, 111, 51, 1, 41, 22, 70, 17, 49, 15, 74, 55, 6, 154, 25, 78, 8, 65, 21, 59, 48, 73, 5, 28, 31, 20, 135, 27, 63, 89, 174, 445, 33, 9, 120, 111, 66

Offset: 0

Author

N. J. A. Sloane, Dec 14 2017; corrected and extended Dec 17 2017

Keywords

• nonn
• base
• look

Comments

A296354(n) is the official position where the binary expansion of n appears in A076478, but the binary expansion of n may also appear earlier, by accident, and it is that starting position that is listed here.

In fact every number > 1 appears earlier - see A296356 for the proof.

Examples

			Here is the list A076478 broken up to show the successive binary numbers (the indexing starts at 0):
0,
1,
0,0,
0,1,
1,0,
1,1,
0,0,0,
0,0,1,
0,1,0,
0,1,1,
1,0,0,
1,0,1,
...
2 = 1,0 officially starts at position 6, so A076478(2) = 6, but 1,0 actually can be seen starting at position 1, so a(2) = 1.
4 = 1,0,0 officially starts at position 22, so A076478(4) = 22, but 1,0,0 actually can be seen starting at position 1, so a(4) = 1.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..16384
• Rémy Sigrist, Perl program for A296355

Crossrefs

Cf. A076478, A061168. A296354, A296356.

Extensions

More terms from Rémy Sigrist, Dec 19 2017